imo class 12 continuity and differentiability

If sin y = x sin(a + y), then dy/dx is:

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If sin y = x sin(a + y), then dy/dx is:

  • A. sin²(a+y)/sin a
  • B. sin a/sin²(a+y)
  • C. sin(a+y)/sin a
  • D. sin a/sin(a+y)

Answer: A) sin²(a+y)/sin a

Explanation: Differentiate: cos y y′ = sin(a+y) + x cos(a+y) y′. Also x = sin y/sin(a+y). Substitute and simplify to get y′ = sin²(a+y)/sin a.

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